This Article 
 Bibliographic References 
 Add to: 
Texture Modeling by Multiple Pairwise Pixel Interactions
November 1996 (vol. 18 no. 11)
pp. 1110-1114

Abstract—A Markov random field model with a Gibbs probability distribution (GPD) is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures. The model takes into account only multiple short- and long-range pairwise interactions between the gray levels in the pixels. An effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the GPD as desired parameters. The scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation. Experiments in modeling natural textures show the utility of the proposed model.

[1] M.B. Averintsev, "Description of Markov Random Fields Using Gibbs Conditional Probabilities," Probability Theory and Its Applications, vol. XVII, no. 1, pp. 21-35, 1972. In Russian.
[2] O. Barndorff-Nielsen, Information and Exponential Families in Statistical Theory. Wiley, 1978.
[3] J.E. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistical Soc., vol. B36, pp. 192-236, 1974.
[4] P. Brodatz, Textures: A Photographic Album for Artists and Designers.New York: Dover Publications, 1966.
[5] R.L. Dobrushin and S.A. Pigorov, "Theory of Random Fields," Proc. 1975 IEEE-USSR Joint Workshop Information Theory, pp. 39-49, Dec.15-19, 1975,Moscow, USSR.New York: IEEE, 1976.
[6] R.C. Dubes and A.K. Jain, "Random Field Models in Image Analysis," J. Applied Statistics, vol. 16, no. 2, pp. 131-164, 1989.
[7] I.M. Elfadel and R.W. Picard, "Gibbs Random Fields, Cooccurrences, and Texture Modeling," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, pp. 24-37, 1994.
[8] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, 1984.
[9] B. Gidas, "Parameter Estimation for Gibbs Distributions from Fully Observed Data," Markov Random Fields: Theory and Applications, R. Chellappa and A. Jain, eds., pp. 471-483.Boston: Academic Press, 1993.
[10] M. Jacobsen, "Existence and Unicity of MLE in Discrete Exponential Family Distributions," Scandinavian J. Statistics, vol. 16, pp. 335-349, 1989.
[11] R.L. Kashyap, "Image Models," Handbook on Pattern Recognition and Image Processing, T.Y. Young and K.-S. Fu, eds., pp. 247-279.Orlando: Academic Press, 1986.
[12] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of State Calculations by Fast Computing Machines," J. Chemical Physics, vol. 21, pp. 1,087-1,091, 1953.
[13] L. Younes, "Estimation and Annealing for Gibbsian Fields," Annales de l'Institut Henri Poincare, vol. 24, no. 2, pp. 269-294, 1988.

Index Terms:
Texture, Markov/Gibbs random field, pairwise interaction, maximum likelihood estimate.
G.l. Gimel'farb, "Texture Modeling by Multiple Pairwise Pixel Interactions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp. 1110-1114, Nov. 1996, doi:10.1109/34.544081
Usage of this product signifies your acceptance of the Terms of Use.